• Corpus ID: 211146507

Dynamics of Cycles in Polyhedra I: The Isolation Lemma

@article{Kessler2020DynamicsOC,
  title={Dynamics of Cycles in Polyhedra I: The Isolation Lemma},
  author={Jan Kessler and Jens M. Schmidt},
  journal={ArXiv},
  year={2020},
  volume={abs/2002.07698}
}
A cycle $C$ of a graph $G$ is \emph{isolating} if every component of $G-V(C)$ is a single vertex. We show that isolating cycles in polyhedral graphs can be extended to larger ones: every isolating cycle $C$ of length $6 \leq |E(C)| < \left \lfloor \frac{2}{3}(|V(G)|+4) \right \rfloor$ implies an isolating cycle $C'$ of larger length that contains $V(C)$. By "hopping" iteratively to such larger cycles, we obtain a powerful and very general inductive motor for proving long cycles and computing… 

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